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The Poggendorff illusion is investigated as a function of the orientation of the stimulus. The stimulus was rotated in steps, starting from alpha = 0° via 90° (vertical bar) to 180°. On the average, the increment was 7.2°. One of the protruding ends of the crossing line served as the target. The angle with the occluding bar was 45°. Observations have been performed on four different variants of the stimulus. One was the classic stimulus, with the protruding ends of the crossing line being collinear. In another variant one of the line segments was omitted. In two more experiments one segment was shifted (up or down), staying parallel to the target line. Compared with the true orientation of the target, deviations of its imaginary continuation up to more than 10° have been found. The illusion approaches a minimum around 45° and 135°. To first order, the experimental results can be approximated by a function ~cos(4alpha). The residuals can be fitted with a function ~sin(alpha). Results are discussed from the point of view that the illusion may be not based on an imaginary tilt or shift of the protruding ends of the transversal, but is due to a strategy of the visual system to decide for the most probable continuation across the bar, not necessarily being collinear to the target line. A conceptual model is presented where the illusion is attributed to a combination of two effects.